{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Orbital Elements\n",
    "\n",
    "**Note:  All angles for orbital elements are in radians**\n",
    "\n",
    "We can add particles to a simulation by specifying cartesian components:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-31T16:04:37.673734Z",
     "start_time": "2023-10-31T16:04:37.647297Z"
    }
   },
   "outputs": [],
   "source": [
    "import rebound\n",
    "sim = rebound.Simulation()\n",
    "sim.add(m=1., x=1., vz = 2.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Any components not passed automatically default to 0.  REBOUND can also accept orbital elements.  \n",
    "\n",
    "**Reference bodies**\n",
    "\n",
    "As a reminder, there is a one-to-one mapping between (x,y,z,vx,vy,vz) and orbital elements, and one should always specify what the orbital elements are referenced against (e.g., the central star, the system's barycenter, etc.).  The differences between orbital elements referenced to these centers differ by $\\sim$ the mass ratio of the largest body to the central mass.  By default, REBOUND always uses Jacobi elements, which for each particle are always referenced to the center of mass of all particles with lower index in the simulation. \n",
    "\n",
    "For the painstaking user: When separating out the center of mass degree of freedom and reducing the N body problem to N-1 Kepler problems and interaction terms, there are a number of possible Hamiltonian splittings (see e.g., Hernandez & Dehnen 2017), and different possible choices for the primary mass in each of the separate Kepler problems. REBOUND takes this primary mass to be the total mass of all the particles in the simulation. If particles are added from the inside out, this gives logical behavior in the limit of a hierarchical system, even for large masses (one can think of it as setting up our new particle in a 2-body orbit around all the interior mass concentrated at the interior particles' center of mass). \n",
    "\n",
    "Let's set up a stellar binary,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-31T16:04:40.389981Z",
     "start_time": "2023-10-31T16:04:40.385507Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------------------------------\n",
      "REBOUND version:     \t4.0.3\n",
      "REBOUND built on:    \tJan 12 2024 08:52:18\n",
      "Number of particles: \t2\n",
      "Selected integrator: \tias15\n",
      "Simulation time:     \t0.0000000000000000e+00\n",
      "Current timestep:    \t0.001000\n",
      "---------------------------------\n",
      "<rebound.particle.Particle object at 0x105a4dac0, m=1.0 x=1.0 y=0.0 z=0.0 vx=0.0 vy=0.0 vz=2.0>\n",
      "<rebound.particle.Particle object at 0x105a4d8c0, m=1.0 x=2.0 y=0.0 z=0.0 vx=0.0 vy=1.4142135623730951 vz=2.0>\n",
      "---------------------------------\n"
     ]
    }
   ],
   "source": [
    "sim.add(m=1., a=1.)\n",
    "sim.status(showAllFields=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We always have to pass a semimajor axis (to set a length scale), but any other elements are by default set to 0.  Notice that our second star has the same vz as the first one due to the default Jacobi elements.  Now we could add a distant planet on a circular orbit,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-31T16:04:42.146464Z",
     "start_time": "2023-10-31T16:04:42.143177Z"
    }
   },
   "outputs": [],
   "source": [
    "sim.add(m=1.e-3, a=100.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This planet is set up relative to the binary center of mass (again due to the Jacobi coordinates), which is probably what we want.  But imagine we now want to place a test mass in a tight orbit around the second star.  If we passed things as above, the orbital elements would be referenced to the binary/outer-planet center of mass.  We can override the default by explicitly passing a primary (any instance of the Particle class):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-31T16:04:43.494998Z",
     "start_time": "2023-10-31T16:04:43.489556Z"
    }
   },
   "outputs": [],
   "source": [
    "sim.add(primary=sim.particles[1], a=0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All simulations are performed in Cartesian elements, so to avoid the overhead, REBOUND does not update particles' orbital elements as the simulation progresses.  However, you can always access any orbital element through, e.g., `sim.particles[1].inc` (see the diagram, and table of orbital elements under the Orbit structure at httsp://rebound.readthedocs.org/en/latest/python_api.html).  This will calculate that orbital element individually--you can calculate all the particles' orbital elements at once with `sim.orbits()`.  REBOUND will always output angles in the range $[-\\pi,\\pi]$, except the inclination which is always in $[0,\\pi]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-31T16:04:45.249652Z",
     "start_time": "2023-10-31T16:04:45.245411Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0000000000000002\n",
      "<rebound.Orbit instance, a=1.0000000000000002 e=2.220446049250313e-16 inc=0.0 Omega=0.0 omega=0.0 f=0.0>\n",
      "<rebound.Orbit instance, a=100.0000000000001 e=1.0403139286217734e-15 inc=0.0 Omega=0.0 omega=0.0 f=0.0>\n",
      "<rebound.Orbit instance, a=-0.018887854728438246 e=25.355597505396737 inc=0.0 Omega=0.0 omega=0.0 f=0.0>\n"
     ]
    }
   ],
   "source": [
    "print(sim.particles[1].a)\n",
    "orbits = sim.orbits()\n",
    "for orbit in orbits:\n",
    "    print(orbit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that there is always one less orbit than there are particles, since orbits are only defined between pairs of particles.  We see that we got the first two orbits right, but the last one is way off.  The reason is that again the REBOUND default is that we always get Jacobi elements.  But we initialized the last particle relative to the second star, rather than the center of mass of all the previous particles.\n",
    "\n",
    "To get orbital elements relative to a specific body, you can manually use the `orbit` method of the Particle class:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-31T16:04:46.285633Z",
     "start_time": "2023-10-31T16:04:46.281830Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<rebound.Orbit instance, a=0.009999999999999573 e=2.131628207280255e-14 inc=0.0 Omega=0.0 omega=3.141592653589793 f=3.141592653589793>\n"
     ]
    }
   ],
   "source": [
    "print(sim.particles[3].orbit(primary=sim.particles[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "though we could have simply avoided this problem by adding bodies from the inside out (second star, test mass, first star, circumbinary planet).\n",
    "\n",
    "When you access orbital elements individually, e.g., `sim.particles[1].inc`, you always get Jacobi elements.  If you need to specify the primary, you have to do it with `sim.orbit()` as above.\n",
    "\n",
    "**Edge cases and orbital element sets**\n",
    "\n",
    "Different orbital elements lose meaning in various limits, e.g., a planar orbit and a circular orbit.  REBOUND therefore allows initialization with several different types of variables that are appropriate in different cases.  It's important to keep in mind that the procedure to initialize particles from orbital elements is not exactly invertible, so one can expect discrepant results for elements that become ill-defined.  For example, "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-31T16:04:46.961943Z",
     "start_time": "2023-10-31T16:04:46.956924Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<rebound.Orbit instance, a=0.9999999999999991 e=5.552131893060635e-16 inc=0.09999999999999945 Omega=0.29999999999999977 omega=3.2607309416278603 f=3.122454365551725>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sim = rebound.Simulation()\n",
    "sim.add(m=1.)\n",
    "sim.add(a=1., e=0., inc=0.1, Omega=0.3, omega=0.1)\n",
    "sim.particles[1].orbit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The problem here is that $\\omega$ (the angle from the ascending node to pericenter) is ill-defined for a circular orbit, so it's not clear what we mean when we pass it, and we get spurious results for both $\\omega$ and $f$, since the latter is also undefined as the angle from pericenter to the particle's position.  However, the true longitude $\\theta$, the broken angle from the $x$ axis to the ascending node = $\\Omega + \\omega + f$, and then to the particle's position, is always well-defined:  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-31T16:04:47.904555Z",
     "start_time": "2023-10-31T16:04:47.901197Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.3999999999999986\n"
     ]
    }
   ],
   "source": [
    "print(sim.particles[1].theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To be clearer and ensure we get the results we expect, we could instead pass theta to specify the longitude we want, e.g."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-31T16:04:48.648906Z",
     "start_time": "2023-10-31T16:04:48.644188Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.3999999999999986\n"
     ]
    }
   ],
   "source": [
    "sim = rebound.Simulation()\n",
    "sim.add(m=1.)\n",
    "sim.add(a=1., e=0., inc=0.1, Omega=0.3, theta = 0.4)\n",
    "print(sim.particles[1].theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-31T16:04:49.053002Z",
     "start_time": "2023-10-31T16:04:49.046366Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<rebound.Orbit instance, a=0.9999999999999998 e=0.19999999999999982 inc=0.0 Omega=0.0 omega=0.09999999999999964 f=8.881784197001252e-16>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import rebound\n",
    "sim = rebound.Simulation()\n",
    "sim.add(m=1.)\n",
    "sim.add(a=1., e=0.2, Omega=0.1)\n",
    "sim.particles[1].orbit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we have a planar orbit, in which case the line of nodes becomes ill-defined, so $\\Omega$ is not a good variable, but we pass it anyway!  In this case, $\\omega$ is also undefined since it is referenced to the ascending node.  Here we get that now these two ill-defined variables get flipped.  The appropriate variable is pomega ($\\varpi = \\Omega + \\omega$), which is the angle from the $x$ axis to pericenter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-31T16:04:50.157271Z",
     "start_time": "2023-10-31T16:04:50.153551Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.09999999999999945\n"
     ]
    }
   ],
   "source": [
    "print(sim.particles[1].pomega)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can specify the pericenter of the orbit with either $\\omega$ or $\\varpi$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-31T16:04:50.786246Z",
     "start_time": "2023-10-31T16:04:50.781876Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<rebound.Orbit instance, a=0.9999999999999998 e=0.19999999999999982 inc=0.0 Omega=0.0 omega=0.09999999999999964 f=8.881784197001252e-16>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import rebound\n",
    "sim = rebound.Simulation()\n",
    "sim.add(m=1.)\n",
    "sim.add(a=1., e=0.2, pomega=0.1)\n",
    "sim.particles[1].orbit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that if the inclination is exactly zero, REBOUND sets $\\Omega$ (which is undefined) to 0, so $\\omega = \\varpi$.  \n",
    "\n",
    "Finally, we can specify the position of the particle along its orbit using mean (rather than true) longitudes or anomalies (for example, this might be useful for  resonances).  We can either use the mean anomaly $M$, which is referenced to pericenter (again ill-defined for circular orbits), or its better-defined counterpart the mean longitude `l` $= \\lambda = \\Omega + \\omega + M$, which is analogous to $\\theta$ above,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-31T16:04:51.821603Z",
     "start_time": "2023-10-31T16:04:51.816066Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.4000000000000039\n",
      "0.39999999999999947\n"
     ]
    }
   ],
   "source": [
    "sim = rebound.Simulation()\n",
    "sim.add(m=1.)\n",
    "sim.add(a=1., e=0.1, Omega=0.3, M = 0.1)\n",
    "sim.add(a=1., Omega=0.3, l = 0.4)\n",
    "print(sim.particles[1].l)\n",
    "print(sim.particles[2].l)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "REBOUND calculates the mean longitude in such a way that it smoothly approaches $\\theta$ in the limit of $e\\rightarrow0$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-31T16:04:52.435713Z",
     "start_time": "2023-10-31T16:04:52.423600Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.39999999999999947"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sim.particles[2].theta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In summary, you can specify the phase of the orbit through any one of the angles `M`, `f`, `theta` or `l`=$\\lambda$.  Additionally, one can instead use the time of pericenter passage `T`.  This time should be set in the appropriate time units, and you'd initialize `sim.t` to the appropriate time you want to start the simulation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Accuracy**\n",
    "\n",
    "As a test of accuracy and demonstration of issues related to the last section, let's test the numerical stability by initializing particles with small eccentricities and true anomalies, computing their orbital elements back, and comparing the relative error.  We choose the inclination and node longitude randomly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-31T16:05:05.189246Z",
     "start_time": "2023-10-31T16:05:05.182572Z"
    }
   },
   "outputs": [],
   "source": [
    "import random\n",
    "import numpy as np\n",
    "\n",
    "def simulation(par):\n",
    "    e,f = par\n",
    "    e = 10**e\n",
    "    f = 10**f\n",
    "    sim = rebound.Simulation()\n",
    "    sim.add(m=1.)\n",
    "    a = 1.\n",
    "    inc = random.random()*np.pi\n",
    "    Omega = random.random()*2*np.pi\n",
    "    sim.add(m=0.,a=a,e=e,inc=inc,Omega=Omega, f=f)\n",
    "    o=sim.particles[1].orbit()\n",
    "    if o.f < 0: # avoid wrapping issues\n",
    "        o.f += 2*np.pi\n",
    "    err = max(np.fabs(o.e-e)/e, np.fabs(o.f-f)/f)\n",
    "    return err"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use the multiprocess module to run the computation in parallel. If the following line throws you an ImportError, install the module with `pip install multiprocess`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-31T16:05:08.599684Z",
     "start_time": "2023-10-31T16:05:08.579075Z"
    }
   },
   "outputs": [],
   "source": [
    "from multiprocess import Pool"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-31T16:05:10.333965Z",
     "start_time": "2023-10-31T16:05:10.155442Z"
    }
   },
   "outputs": [],
   "source": [
    "random.seed(1)\n",
    "N = 100\n",
    "es = np.linspace(-16.,-1.,N)\n",
    "fs = np.linspace(-16.,-1.,N)\n",
    "params = [(e,f) for e in es for f in fs]\n",
    "with Pool() as pool:\n",
    "    res = pool.map(simulation, params)\n",
    "    res = np.array(res).reshape(N,N)\n",
    "    res = np.nan_to_num(res)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-31T16:05:13.391051Z",
     "start_time": "2023-10-31T16:05:12.855469Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import ticker\n",
    "from matplotlib.colors import LogNorm\n",
    "import matplotlib\n",
    "\n",
    "f,ax = plt.subplots(1,1,figsize=(7,5))\n",
    "extent=[fs.min(), fs.max(), es.min(), es.max()]\n",
    "\n",
    "ax.set_xlim(extent[0], extent[1])\n",
    "ax.set_ylim(extent[2], extent[3])\n",
    "ax.set_xlabel(r\"true anomaly (f)\")\n",
    "ax.set_ylabel(r\"eccentricity\")\n",
    "\n",
    "im = ax.imshow(res, norm=LogNorm(vmax=1., vmin=1.e-16), aspect='auto', origin=\"lower\", interpolation='nearest', cmap=\"RdYlGn_r\", extent=extent)\n",
    "cb = plt.colorbar(im, ax=ax)\n",
    "cb.solids.set_rasterized(True)\n",
    "cb.set_label(\"Relative Error\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the behavior is poor, which is physically due to $f$ becoming poorly defined at low $e$.  If instead we initialize the orbits with the true longitude $\\theta$ as discussed above, we get much better results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-31T16:05:22.873572Z",
     "start_time": "2023-10-31T16:05:22.442522Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def simulation(par):\n",
    "    e,theta = par\n",
    "    e = 10**e\n",
    "    theta = 10**theta\n",
    "    sim = rebound.Simulation()\n",
    "    sim.add(m=1.)\n",
    "    a = 1.\n",
    "    inc = random.random()*np.pi\n",
    "    Omega = random.random()*2*np.pi\n",
    "    omega = random.random()*2*np.pi\n",
    "    sim.add(m=0.,a=a,e=e,inc=inc,Omega=Omega, theta=theta)\n",
    "    o=sim.particles[1].orbit()\n",
    "    if o.theta < 0:\n",
    "        o.theta += 2*np.pi\n",
    "    err = max(np.fabs(o.e-e)/e, np.fabs(o.theta-theta)/theta)\n",
    "    return err\n",
    "\n",
    "random.seed(1)\n",
    "N = 100\n",
    "es = np.linspace(-16.,-1.,N)\n",
    "thetas = np.linspace(-16.,-1.,N)\n",
    "params = [(e,theta) for e in es for theta in thetas]\n",
    "\n",
    "with Pool() as pool:\n",
    "    res = pool.map(simulation, params)\n",
    "    res = np.array(res).reshape(N,N)\n",
    "    res = np.nan_to_num(res)\n",
    "\n",
    "f,ax = plt.subplots(1,1,figsize=(7,5))\n",
    "extent=[thetas.min(), thetas.max(), es.min(), es.max()]\n",
    "\n",
    "ax.set_xlim(extent[0], extent[1])\n",
    "ax.set_ylim(extent[2], extent[3])\n",
    "ax.set_xlabel(r\"true longitude (\\theta)\")\n",
    "ax.set_ylabel(r\"eccentricity\")\n",
    "\n",
    "im = ax.imshow(res, norm=LogNorm(vmax=1., vmin=1.e-16), aspect='auto', origin=\"lower\", interpolation='nearest', cmap=\"RdYlGn_r\", extent=extent)\n",
    "cb = plt.colorbar(im, ax=ax)\n",
    "cb.solids.set_rasterized(True)\n",
    "cb.set_label(\"Relative Error\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Hyperbolic & Parabolic Orbits**\n",
    "\n",
    "REBOUND can also handle hyperbolic orbits, which have negative $a$ and $e>1$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-31T16:05:26.698969Z",
     "start_time": "2023-10-31T16:05:26.691959Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------------------------------\n",
      "REBOUND version:     \t4.0.3\n",
      "REBOUND built on:    \tJan 12 2024 08:52:18\n",
      "Number of particles: \t4\n",
      "Selected integrator: \tias15\n",
      "Simulation time:     \t0.0000000000000000e+00\n",
      "Current timestep:    \t0.001000\n",
      "---------------------------------\n",
      "<rebound.particle.Particle object at 0x10c411440, m=1.0 x=0.0 y=0.0 z=0.0 vx=0.0 vy=0.0 vz=0.0>\n",
      "<rebound.particle.Particle object at 0x10c4112c0, m=0.0 x=0.821318061318507 y=0.3695219671870099 z=0.0 vx=-0.44206687767576147 vy=1.0125602418928732 vz=0.0>\n",
      "<rebound.particle.Particle object at 0x10c411440, m=0.0 x=0.9210609940028852 y=0.38941834230865013 z=0.0 vx=-0.38941834230865013 vy=0.9210609940028852 vz=0.0>\n",
      "<rebound.particle.Particle object at 0x10c4112c0, m=0.0 x=0.07999999999999999 y=0.0 z=0.0 vx=0.0 vy=5.477225575051662 vz=0.0>\n",
      "---------------------------------\n",
      "The following fields have non-default values:\n",
      "N:\n",
      "\u001b[31m< 0\u001b[0m\n",
      "---\n",
      "\u001b[32m> 4\u001b[0m\n",
      "rand_seed:\n",
      "\u001b[31m< 620290\u001b[0m\n",
      "---\n",
      "\u001b[32m> 778246\u001b[0m\n",
      "particles:\n",
      "\u001b[32m> (512 bytes, values not printed)\u001b[0m\n",
      "\n"
     ]
    }
   ],
   "source": [
    "sim.add(a=-0.2, e=1.4)\n",
    "sim.status()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Currently there is no support for exactly parabolic orbits, but we can get a close approximation by passing a nearby hyperbolic orbit where we can specify the pericenter = $|a|(e-1)$ with $a$ and $e$.  For example, for a 0.1 AU pericenter,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-31T16:05:33.467627Z",
     "start_time": "2023-10-31T16:05:33.462702Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<bound method Particle.orbit of <rebound.particle.Particle object at 0x10c4112c0, m=0.0 x=0.1110223024625156 y=0.0 z=0.0 vx=0.0 vy=4.244337228529561 vz=0.0>>\n"
     ]
    }
   ],
   "source": [
    "sim = rebound.Simulation()\n",
    "sim.add(m=1.)\n",
    "q = 0.1\n",
    "a=-1.e14\n",
    "e=1.+q/np.fabs(a)\n",
    "sim.add(a=a, e=e)\n",
    "print(sim.particles[1].orbit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Retrograde Orbits**\n",
    "\n",
    "Orbital elements can be counterintuitive for retrograde orbits, but REBOUND tries to sort them out consistently.  This can lead to some initially surprising results.  For example,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-31T16:05:35.112999Z",
     "start_time": "2023-10-31T16:05:35.107330Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<bound method Particle.orbit of <rebound.particle.Particle object at 0x10c411440, m=0.0 x=0.48627207528132577 y=0.7573238863271068 z=-9.274542733083253e-17 vx=0.9302811761928806 vy=-0.5973266739761528 vz=7.315141993302302e-17>>\n"
     ]
    }
   ],
   "source": [
    "sim = rebound.Simulation()\n",
    "sim.add(m=1.)\n",
    "sim.add(a=1.,inc=np.pi,e=0.1, Omega=0., pomega=1.)\n",
    "print(sim.particles[1].orbit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We passed $\\Omega=0$ and $\\varpi=1.$.  For prograde orbits, $\\varpi = \\Omega + \\omega$, so we'd expect $\\omega = 1$, but instead we get $\\omega=-1$.  If we think about things physically, $\\varpi$ is the angle from the $x$ axis to pericenter, measured in the positive direction (counterclockwise) defined by $z$.  $\\Omega$ is always measured in this same sense, but $\\omega$ is always measured in the orbital plane *in the direction of the orbit*.  For retrograde orbits, this means that $\\omega$ is measured in the opposite sense to $\\Omega$, so $\\varpi = \\Omega - \\omega$, which is why we got $\\omega = -1$. \n",
    "\n",
    "Similarly, the retrograde version of $\\theta = \\Omega + \\omega + f$ is $\\theta = \\Omega - \\omega - f$, and `l` = $\\lambda = \\Omega + \\omega + M$ becomes $\\lambda = \\Omega - \\omega - M$.  REBOUND chooses these conventions based on whether $i < \\pi/2$, which means that if you were tracking $\\varpi$ for nearly polar orbits, you would get unphysical jumps if the orbits crossed back and forth between prograde and retrograde.  Of course, $\\varpi$ is not a good angle at such high inclinations, and only has physical meaning when the orbital plane nearly coincides with the reference plane."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exceptions**\n",
    "\n",
    "Adding a particle or getting orbital elements from particles in a simulation should never yield NaNs in any of the structure fields.  Please let us know if you find a case that does.  \n",
    "\n",
    "In cases where it would return a `NaN`, `REBOUND` will raise a `ValueError`.  The only cases that should do so when adding a particle are 1) passing an eccentricity of exactly 1. 2) passing a negative eccentricity. 3) Passing $e>1$ if $a>0$. 4) Passing $e<1$ if $a<0$. 5) Passing a longitude or anomaly for a hyperbolic orbit that's beyond the range allowed by the asymptotes defined by the hyperbola.  You will also get errors if you try to initialize particles with orbital elements manually with `rebound.Particle()`.\n",
    "\n",
    "When obtaining orbital elements from a `Particle` structure, REBOUND will raise a `ValueError` if 1) the primary's mass is zero, or 2) the particle's and primary's position are the same.\n",
    "\n",
    "**Negative inclinations**\n",
    "\n",
    "While inclinations are only defined in the range $[0,\\pi]$, you can also pass negative inclinations when adding particles in REBOUND.  This is interpreted as referencing $\\Omega$ and $\\omega$ to the **descending**, rather than the ascending node.  So for example, if one set up particles with the same $\\Omega$ and a range of inclinations distributed around zero, one would obtain what one might expect, i.e. a set of orbits that are all rotated around the same line of nodes.\n",
    "\n",
    "**Jacobi masses**\n",
    "\n",
    "There is a classical Hamiltonian splitting for the N-body problem (see e.g., Wisdom & Holman 1991) that when expanded to first order in the planet/star mass ratio, gives an interaction Hamiltonian with the same form as the disturbing function for an exterior perturber. This makes it particularly attractive for analytic or semi-analytic studies. In this splitting, the masses of the primaries for each planet take on a particular form. One can add particles using these jacobi masses with the `jacobi_masses` flag. By default, this flag is false and the primary mass is the total mass of all particles in the simulation (see the top of this notebook)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-31T16:05:37.091245Z",
     "start_time": "2023-10-31T16:05:37.086813Z"
    }
   },
   "outputs": [],
   "source": [
    "import rebound\n",
    "sim = rebound.Simulation()\n",
    "sim.add(m=1.)\n",
    "sim.add(m=1.e-3, a=1., jacobi_masses=True)\n",
    "sim.add(m=1.e-3, a=5., jacobi_masses=True)\n",
    "sim.move_to_com()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The jacobi mass and default mass assigned by REBOUND always agree for the first particle, but differ for all the rest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-31T16:05:38.102446Z",
     "start_time": "2023-10-31T16:05:38.098406Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0 4.995009980039918\n"
     ]
    }
   ],
   "source": [
    "print(sim.particles[1].a, sim.particles[2].a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can calculate orbital elements using jacobi masses by using the same flag in `sim.orbits`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-10-31T16:05:38.958306Z",
     "start_time": "2023-10-31T16:05:38.954331Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0 4.999999999999999\n"
     ]
    }
   ],
   "source": [
    "o = sim.orbits(jacobi_masses=True)\n",
    "print(o[0].a, o[1].a)"
   ]
  }
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